One of the most used methods for numerically evaluating the contribution of each Feynman diagram is diagrammatic Monte Carlo (DiagMC) [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. This method has been developed, and one of the powerful simplifications is to deal with the Hugenholtz diagrams [7]}, which is the combination between direct and exchange potential, instead of ordinary Feynman diagrams [8]}, [9]}. This improvement has two advantages. First, it is directly processed with the essentially distinct diagram (EDD) chosen from its equivalent diagrams because the standard DiagMC method samples the diagrams one by one. Second, these smaller numbers of Hugenholtz diagrams increase the efficiency of Monte Carlo sampling and decrease the computation cost. In this case, our previous fast algorithm [10]} could be used to generate all EDDs.
